I. Functions

① linear function: y=kx+b

② quadratic function: y = ax 2+bx+c

③ Inverse proportional function: y=k/x direct proportional function; Y=kx when b=0.

④ exponential function: y = a x (a > 0 and not equal to 1)

⑤ logarithmic function: y = loga x loga1= ologaa =1.

Second, the derivation formulas of several common functions

①C'=0(C is a constant)

②(x^n)'=nx^(n- 1) (n∈Q)

③(sinx)'=cosx

④(cosx)'=-sinx

⑤(e^x)'=e^x

⑥ (a x)' = a A Xin (ln is natural logarithm).

Three, four algorithms of derivative

①(u v)'=u' v '

②(uv)'=u'v+uv '

③(u/v)'=(u'v-uv')/ v^2

Fourth, the derivative function of composite function

① Let y = u (t) and t = v (x), then y'(x) = u'(t)v'(x) = u' v'(x).

For example: y = t^2, t = sinx, then y'(x) = 2t * cosx = 2sinx*cosx = sin2x.